We propose an algebraic model of computation which formally relates symbolic listings, complexity of Boolean functions, and low depth arithmetic circuit complexity. In this model algorithms are arithmetic formula expressing symbolic listings of YES instances of Boolean functions, and computation is executed via partial differential operators. We consider the Chow rank of an arithmetic formula as a measure of complexity and establish the Chow rank of multilinear polynomials with totally non-overlapping monomial support. We also provide Chow rank non-decreasing transformations from sets of graphs to sets of functional graphs.

翻译：我们提出一种代数计算模型，该模型将符号列表、布尔函数复杂度与低深度算术电路复杂度形式化地关联起来。在该模型中，算法被定义为表示布尔函数YES实例符号列表的算术公式，计算过程通过偏微分算子执行。我们将算术公式的Chow秩作为复杂度度量，并建立了具有完全不重叠单项式支撑的多线性多项式的Chow秩。此外，我们还提供了从图集合到泛函图集合的Chow秩非递减变换。